Kolmogorov–Arnold Transformer Koopman Modeling Approach to Unknown Nonlinear Robotic Systems

Abstract

This article presents a Kolmogorov–Arnold transformer Koopman modeling (KATKM) approach for unknown nonlinear robotic systems. Specifically, a Kolmogorov–Arnold transformer (KAT) is developed by introducing the Kolmogorov–Arnold network (KAN) into the Transformer encoder to efficiently capture spatial dynamic dependencies among system states. In addition, a KAN Koopman predictor is developed to directly learn Koopman observable functions by parameterizing B-spline activation functions. Experimental evaluations on robotic manipulators show that KATKM outperforms state-of-the-art Koopman-based methods in prediction accuracy, trajectory tracking, and robustness against measurement noise.